Put into bat, Sri Lanka were allout for 236 but they still managed to put pressure on Pakistan, who were left toterring at 162-7 at one stage.
But Sri Lankan fielders dropped Sarfraz Ahmed twice off Lasith Malinga's overs as the Pakistan skipper cracked a match-winning 61 to take his team to the semifinals.
"It was a bit of a funny wicket. We hadn't got the runs on the board but we knew we could defend this. And the bowlers did their job, but we didn't hold on to our catches," he said.
"A see-saw kind of a game. Credit should go to Pakistan. They held their nerves and are deserved winners."
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The Sri Lankan captain, however, backed his inexperienced team for trying to defend the modest total.
"Proud of the boys. Even though we only had 236 to defend, they gave it their all. Unfortunately, we missed a few chances. In a big tournament like this, they fought hard an inexperienced team. I'm proud of them," he said.
Sarfraz heaped praise on Mohammad Amir for hanging on till the end as they shared a 75-run partnership for the eighth wicket.
Sarfraz, who was adjudged Man of the Match, was dropped twice in the 39th and 41st over off Malinga.
"Drop catches are part of the game. Allah helped us and that's why Pakistan won today," he said.